**Solution:**

Given:
Initial velocity, u = 10 m/s
Coefficient of kinetic friction, μ = 0.10

To find:
The distance traveled before coming to rest.

**Analysis:**

When a block is projected along a rough horizontal road, the force of kinetic friction acts in the opposite direction to the motion of the block. This force can be calculated using the equation:

**F(friction) = μ * F(normal)**

where F(normal) is the normal force acting on the block.

The normal force is equal to the weight of the block, which can be calculated using the equation:

**F(normal) = m * g**

where m is the mass of the block and g is the acceleration due to gravity.

The force of kinetic friction can also be expressed as:

**F(friction) = μ * m * g**

The work done by the force of kinetic friction is given by the equation:

**Work done = Force * Distance**

In this case, the work done by the force of kinetic friction is equal to the change in kinetic energy. Therefore, we can write:

**Work done = Change in kinetic energy**

Since the block comes to rest, the final velocity is 0. Therefore, the change in kinetic energy is given by:

**Change in kinetic energy = 0.5 * m * (v^2 - u^2)**

where v is the final velocity.

**Calculation:**

We know that the work done by the force of kinetic friction is equal to the change in kinetic energy. Therefore, we can write:

**μ * m * g * d = 0.5 * m * (v^2 - u^2)**

The mass of the block cancels out:

**μ * g * d = 0.5 * (v^2 - u^2)**

Since the block comes to rest, the final velocity v is 0. Therefore, the equation becomes:

**μ * g * d = 0.5 * (0^2 - u^2)**

Simplifying the equation further, we get:

**μ * g * d = -0.5 * u^2**

Solving for distance d, we find:

**d = (-0.5 * u^2) / (μ * g)**

Plugging in the values u = 10 m/s, μ = 0.10, and g = 9.8 m/s^2, we can calculate the distance traveled before coming to rest:

**d = (-0.5 * (10^2)) / (0.10 * 9.8)**

**d ≈ -5.10 meters**

Since distance cannot be negative, we take the absolute value:

**d ≈ 5.10 meters**

Therefore, the block will travel approximately 5.10 meters before coming to rest.